What is Maclaurin Series

The Maclaurin series formula is a special case of the Taylor series formula. Or in other words, we can derive the Maclaurin formula from the Taylor series very easily.

Maclaurin series formula helps in writing a function as a series (or sum) of terms involving the derivatives of the function. This formula helps in finding the approximate value of the function.

Maclaurin series formula

ex =1 + x + x2/2! + x3/3! + ……

What is Maclaurin Series formula.
Maclaurin Series formula
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How to find Maclaurin Series Formula

We can find or Derive the Maclaurin series from Taylor series.

Sol. As we Know Taylor series is:

taylor series formula
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Let f(x) = ex and f(0)=1 (because we only know value of f at x0=1).

Also f(0) = 1, f’(0) = 1, f’’(0) = 1

Since  (d/dx)ex = ex

Therefore, f’(x) = ex

F’’(x) = ex

F’’’(x) = ex

:

:

Now, f(0+h) = f(0) + f’(0)h + f’’(0)h2/2! + f’’’(0)h3/3!

F(h) = 1 + h + h2/2 + h3/6 + h4/24 + …

x+h = 0 +h, ( or replace h by x).

f(x) = 1 + x + x2/2 + x3/6 + x4/24 + ….

Or,  This can be simplified as maclaurin series.

ex =1 + x + x2/2! + x3/3! + ……

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